Process for controlling excess carrier concentration in a semiconductor



United States Patent ice PROCESS FOR CONTROLLING EXCESS CARRIERCONCENTRATION IN A SEMICONDUCTOR George S. Indig, Bronxville, N. Y., andWilliam G. Pfann, Far Hills, N. J., assignors to Bell TelephoneLaboratories, Incorporated, New York, N. Y., a corporation of New YorkNo Drawing. Application June 25, 1957 Serial No. 667,956

12 Claims. (Cl. 148-15) This invention relates to methods for producingbodies of extrlnsic semiconductive material manifesting substantlallyuniform conductivity characteristics within substanconstant conductivitylevel. Since conductivity level in extrinsic semiconductive materialssuch as silicon, gercompensates for the changing example, United StatesPatent 2,768,914. Other methods of compensating for such varyingconcentration within the melt include various mechanisms by which thematerial with respect to which the melt is depleted is gradually addedin such amount as to exactly compensate for the amount removed throughcrystallization.

A second approach utilizes a melt of constant volume and of constantcomposition which is maintained by producing a second solid-liquidinterface which advances into solid material of substantially uniformconcentration at the identical rate of the freezing interface at whichthe crystalline body is being produced. One method of crystallizing fromsuch a constant volume, constant composition melt, sometimes referred toas zone leveling, is described in United States Patent 2,739,088.

The degree of success obtained in the production of a crystalline bodymanifesting uniform resistivity along the growth axis in any one of theabove processes and in any other process utilizing a freezingsolid-liquid interface is dependent upon the precision with which growthcondi tions may be controlled.

The requirement of such precise control over growth conditions such asrate of advancement of the freezing interface, melt temperature at theinterface, and stirring within the melt whether due to natural or forcedconvection, arises out of the existence of a discrete layer of moltenmaterial on the liquid side of the freezing interface within which allcirculation of liquid material takes place exclusively by the diffusionmechanism.

phase, results in either an 2,861,905 Patented Nov. 25, 1958 Thisdiffusion layer, of a thickness in the growth direction to which thesymbol A is here ascribed, is the material from which the crystallinematerial is actually solidified, so that the concentration of anyingredient in the solidifying material is related through thedistribution coeflicient not to the average melt concentration butrather to the concentration of the melt adjacent to the interface withinthe diffusion layer. The thickness of the diffusion layer A is in turndependent upon various factors, all of which are affected by conditionsof growth. Such factors include the diffusion rate of the ingredient ofconcern within the, liquid material which varies with temperature, therate of movement of the freezing interface, and the degree of stirringwithin the melt whether by natural or artificial means. i

direction of growth, the concentration of this ingredient within thislayer increases in the instance of such an;

ingredient having a distribution coefificient less than 1, and decreasesin the instance of an ingredient having a distribution coefficientgreater than 1. Effectively, therefore, as the thickness of thediffusion layer increases, the concentration of such an ingredient inthe layer adjacent the interface varies in such a direction as to opposethe non-uniform distribution between phases dictated by the distributioncoefiicient with reference to the mean melt composition even though thedistribution of such an ingredient at such an interface is always thatdictated by the distribution coefiicient with reference to theconcentration of the liquid material adjacent the interface. virtualimpossibility of measuring the concentration of the liquid at theinterface and the comparative ease of measuring the concentration in thebody of the melt has resulted in a definition of such distributionconditions in terms of body concentration. Since the concentration ofthe body of the melt varies more or less from the concentration at theinterface, depending upon growth conditions, the concentration realizedin the crystallizing material is not that dictated by the equilibriumdistribution coeflicient in terms of body concentration. This has givenrise to use of so-called effective distribution coeificients which areempirically determined and which invariably compare with the equilibriumcoeff cient in that they are numerically closer to 1.

The variations in the value of the effective distribution coefficientrelative to growth rate and stirring rate are known and advantage istaken of such variation in processes known to the art. For example, inthe process known as rate growing an extrinsic semiconductive materialcontaining both p-type and n-type impurity of proper amount iscrystallized from a melt while varying the growth rate under conditionssuch that changes in conductivity type are produced. Changesin theeffective coefiicient are also utilized in the crystal pulling ofconstant resistivity sections of semiconductor materials by increasingor decreasing the rate of growth so as to offset the gradual change incomposition of the melt. q

The methods herein are directed to eliminating overall microscopicnon-uniformity of resistivity. Such microscale fluctuations ofresistivity are a serious problem, especially in transistors and diodesmade by the diffusion technique, for in such cases, very irregular p-njunctions result from microscale resistivity variations in the basematerial.

Prior art developments directed concentration variations in growingcrystals due to random variations in growth conditions have, for themost part, been directed toward elimination of the random variationsthemselves. Such developments include the use of steeper temperaturegradients in the vicinity of the interface, exceedingly slow crystallinegrowth rates, extremely close control of temperature and coolingcontoward eliminating The ditions, and various special furnaceconfigurations. The processes of this invention represent a new approachin that no special attempt is made to eliminate such random variations.In a species of this invention recognition is made of the fact that forthe levels of impurity concentration involved in the usual extrinsicsemiconductor system, the conductivity characteristics including theresistivity of the final crystal are dependent not upon the total amountof such impurity contained, but are dependent on the excess of suchpredominant impurity over any opposite conductivity type inducingmaterial which may be present.

In essence, the processes of this invention attain the objective ofuniform resistivity and uniformity of other conductivity characteristicsby including in the melt from which material is being crystallized botha first significant impurity imparting the desired conductivitycharacteristics and a second significant impurity imparting either thesame or the opposite conductivity characteristics, the second impuritybeing of such character and being included in such amount that randomvariations in growth conditions produce a variation in concentrationlevel of both impurities so that the excess amount of impuritiesimparting the desired conductivity characteristics remain substantiallyconstant in the crystallizing material. If the specific requirements setforth herein are met, these processes operate in identical fashionWhether the second impurity is such as imparts the desired conductivitytype or the opposite conductivity type, the excess impurity in thecrystallized product in the first instance being equal to the sumconcentration of the two impurities and in the second instance beingequal to the difference concentration of the first impurity less thesecond. In this manner, assuming given growth conditions, the uniformityof resistivity of the final product may be improved several orders ofmagnitude over the same growth conditions as applied to a semiconductivematerial containing only the one impurity imparting desired conductivitytype.

The processes of this invention are referred to herein as compensationmethods. The usual system discussed herein comprises, as the majoringredient, a fusible semiconductive material such as germanium orsilicon, a significant impurity imparting the desired conductivity typereferred to herein as the first significant impurity, or first soluteand a second significant impurity or second solute compensating forconcentration variations in the excess significant impurity, referred toherein as the second significant impurity or second solute. Although theinvention is described in terms of such simple ternary systems, it is tobe recognized that the invention is not so limited and may contain bothtypes of second impurities and/or any number of additional ingredientswhich may contribute to the desideratum of uniform resistivity or whichmay serve any other function.

The following discussion is in terms of two solutes, solute l and solute2, one of which is an acceptor and one of which is a donor. Although thederivation differs slightly, the final equations are identical inabsolute value for two acceptor or two donor solutes in accordance withthis invention. The small changes involved are indicated at the end ofthis section.

In this section the properties of the solutes are set forth, expressionsfor critical concentration ratios are developed, and the sensitivity ofthe effect to growth variations and deviations from the critical ratioare indicated.

In this discussion the subscripts l and 2 have reference, respectively,to solutes l and 2, C and C designating melt concentrations of thesesolutes in that order. The symbol k designates the effectivedistribution coefficient or concentration of solute in the solid phasedivided by the concentration of the solute in the bulk liquid. Considera melt containing solutes 1 and 2 of concentrations C and C at a meangrowth rate 7. Let k and k Z k C -k2C The electrical conductivity of thesemiconductor is proportional to this difference concentration. Let theratio R be defined as:

R=C2/C1 Then, from (I) and (2): Z=C (k -Rk 3 Allowing a change, d), ingrowth rate 1 to occur, producing changes dk, and dk in the effectivedistribution coefficient, then:

3? 1( 1-Rdk2) produced by the change in f, R, has the critical There isno change in Z that is, 5Z/5f is zero, if the ratio, value Rt, definedas:

ME (M 29% dlc /df dlc The ratio R is a definite function of growth rate,1, and other variables, and is obtainable from Equation 6, theBurton-Prim-Slichter equation, for the steady state value of theeffective distribution coefficient.

where k denotes the equilibrium value of k, which holds at very lowgrowth rates A denotes effective thickness of diffusion layer incentimeters, and I D denotes diffusivity of the solute in the liquid incentimeters squared per second. From Equation 6, R* can be expressed as:

C d 6 1 dIC2 Multiplying each side of (8) by k k gives:

1% dk k d1nk (9) 76101 in which 8*: the critical ratio in terms ofconcentrations in the solid rather than the liquid phase.

Since the amount of compensating solute is to be less than the amount ofexcess solute 1 in the crystallizing solid, k C is less than k C (Zbeing considered to be positive), and 8* is numerically less than 1. Itis generally-prefera'ble in the processes herein to maintain thefraction compensated, 8*, small. Thi requires that the fractional changeof k with f or A, be relatively large compared with that of k In theprocesses of this invention it is preferred that the concentrations andcharacteristics of solutes be such as to result in the critical ratio,R*. operating conditions are to be preferred, an advantage,nevertheless, exists even where the amount ing solute added is such asto result in a ratio which deviwhere the subscripts denote that R and fhave the values R* and 1 and that the derivative is evaluated at R=R*,f=f*, where f is the growth rate corresponding to R*. Let ratio Rdeviate from the critical value and equal Then 62 in. t n i f af i(1+6)R*df) (11) It is here assumed that the deviation in the value of Rfrom R is brought about through a change in C holding C constant.Therefore,

62 ar a EJERHHC1ER O1df Thus, it is seen that a fractional deviation 6,of R from R*, produces a growth rate coefiicient of Z, which is 6 timesthe growth rate coefiicient of solute 1 alone, which is C (dk /df). Theratio Q of the growth rate coefiicient of Z to that of k C theconcentration of solute 1 alone, where Z equals k C is:

Q (13 It can be seen from Equation 13, that for any value of R from to2R*/(1S), the presence of solute 2 decreases the effect of fluctuationsin f or A on the resistivity. Thus: at R=0, e=+l, and Q=+1; atR=R*/(v-S), 8:0, and Q=0; at R=2R*/(1-S), e=+1, and Q=l; small S isfavored where a low fraction compensated and a low sensitivity to thecritical ratio are desired.

The following indicates the effect of deviations from the criticalgrowth rate F. The above equations apply strictly for small changes inf. If the change in J from f* is sufficiently great, since is the rateat which R* was determined, then dk /dk is no longer equal to R*. Thenew value of the ratio is designated R.

An expression for the fraction R'/R* in terms of f and f-" is developed:

01) 1) 1) 1a! ill) (lc2 L) [fez/D2 02) 2) A corresponding expression canbe Written for dia 1:

by substituting f in the right side of Equation 14. The ratio R/R isfound to be d] J 70 k 2 A %=i iiii iiii lfiiiklli l h -Mae Thisexpression can be set equal to (1+ where:

in a procedure similar to that used in Equation 11. The

eifect of the deviation, 7, of R from R* produced by the change (ff-'f)in growth rate, is evaluated as in Equations 12 and 13.

Although such 6 A useful approximation in the instance of a segregationcoefiicient k equal to or less than 0.1 is:

Fad

Using this approximation it is found that the right side of Equation isequal to unity. Hence, the quantity (fiZ/fif) is quite insensitive togrowth rate where the distribution coefiicients of both impurities isequal to or less than 0.1. This approximation applies, for example, to agermanium system containing gallium and antimony as excess andcompensating impurities. This approximation has been experimentallysubstantiated.

That the method is fairly insensitive to growth rate even where thevalues of the distribution coeflicients are greater than 1 is seen fromthe Assume (A/D )=(A/D Then:

Let f(A/D) =1, Then Hence:

Thus, doubling the growth, so that f=2f*, produces a growth ratecoefiicient of Z that is only 0.3/(1-S) of that for an equalconcentration of solute 1 alone. The factor (1-S) has the samesignificance here as in Equation 13.

The above analysis has been given in terms of changes in f. A similarthickness Table Solute A Solute B Quantity maintained constant Total.

0. Difference. Do.

Acceptor. Donort t Equations defining the requirements of solutematerial are derived above in terms of solutes of opposite con- Since inreality the difference concentration Z in Equation 1 has reference tothe excess majority significant solute which, as is well known in theart, is a measure of the total amount of significant impurity impartingconductivity characteristics to the semiconductive material, Z, may withequal validity be considered to define the total concentration of allsignificant impurities of a given type where opposite conductivity typeimparting solutes are not of concern in the system. Since this conditionapplies to the processes of this invention in which the compensatingsolute 2 is of the same type as solute 1, that is, for either ofinstances 1 or 2 in the above table,

in which Z is the difference concentration and continues to representthe ditierence between concentrations of opposite type solutes, one ofwhich is not of concern here, and in which the other symbols are asdefined above.

With this change in sign of the quantity k C Equation 8 may now berewritten as However, since the concentrations of the solutes 1 and. 2vary in opposite directions with growth rate, in this instance one ofthe two quantities dk and dk is always negative so that C /C is herealso equal to a positive value of dk /dk The remainder of the derivationset forth above is now directly applicable to either of instances 1 and2 of the table above.

Example 1 below is illustrative of the method of determining the properamount of compensating solute to offset variations in growth conditionsin a typical semiconductive system.

Example 1.-From experimental data of Bridgers (Journal of AppliedPhysics, volume 27, pages 746-751 (1956)) for the system germanium plusantimony (a donor, or n-type, impurity) plus gallium (an acceptor,orp-type impurity), it is found that the critical ratio R* has the value0.14 at a growth rate of 0.0025 centimeter per second in av pulledcrystal rotated at 144 R. P. M. Thus, the ratio of melt concentrationsof antimony to gallium, C /C where 2 denotes antimony, is

7. Let the desired concentration in the solid,

Z:k1C1*k2C2, be

corresponding to a p-type resistivity in the solid of about 10ohm-centimeters at room temperature. The values of the ks, at thesegrowth conditions are:

k :0.l05 and k :0.0046

X atoms per centimeter Using the relationship C =7C the required meltconcentration C is given by Z=k C -k C 1.0 X 10 :0.105C 0.0046(.14)C C=1.0 X 10 atoms gallium/centimeters C :7 .0 X 10 atomsantimony/centimeters The fraction compensated, S, is

- rotation rate of 144- R. P. M.

centration increase of gallium in the growth crystal of 25 percentproducing a conductivity deviation of 25 percent.

Consider a germanium system containing gallium as solute 1 and antimonyas solute 2 in amount such that the difference between the two ata meangrowth rate of 0.0025 centimeter per second and a crystal rotation rateof 30 R. P. M. produces a conductivity level the. same as that of thegermanium system above. The quantities of gallium and antimony in themelt are those determined by the critical ratio R in accordance with theequations. The growth rate of the growing crystal is increased 50percent. Under these conditions the variation in differenceconcentration in the growing crystal is less than 1 percent. Thepercentage deviation in conductivity is also less than 1 percent.

Consider a germanium system containing gallium and antimony, the amountsbeing such as to result in the same difference concentration of galliumas that of the system of the first paragraph in this example under theidentical growth conditions. The quantities of gallium and antimony inthe meltt are such as to result in a ratio R equal to i 20 percent.increase the growth rate 50 percent. Under these conditions, the excessgallium concentration in the crystallizing material deviates 6 percentwith the conductivity shownig the same percentage deviation.

Examiple 3.Consider a germanium system containing gallium as the solesignificant impurity with a crystal growth rate of 0.0025 centimeter persecond and a crystal Increasing the growth rate 50 percent results in anincrease in gallium concentration in the growing crystal of 20 percent.

Consider a germanium system containing both gallium and boron assignificant impurities in amounts such that the total concentration ofthe two impurities in the crystallizing material at a mean growth rateof 0.005 centimeter per second and at a crystal rotation rate of 144 R.P. M. is such as to result in a crystal of the same conductivity levelas that of the first paragraph under this example. The amounts ofgallium and boron are such that the concentration of boron in the liquiddivided by the concentration of gallium in the liquid is equal to R*(numerically equal to 0.0038). Increasing the growth rate by 50 percentresults in a conductivity deviation in the growing crystal of less than2 percent.

Consider a germanium gallium-boron system in which the amounts ofgallium and boron in the melt are such as to result in the conductivitylevel of the system of the first paragraph of this example underidentical growth conditions. The amounts of gallium and boron in themelt are further such that the ratio R equals R -:20 percent. Anincrease of 50 percent in the growth rate results in a conductivitydeviation in the growing crystal of about 5 percent.

As is seen from the above examples taken in conjunction with thediscussion herein a deviation in the ratio of the melt concentrations ofsolutes 1 and 2 from the critical value R* although it does not resultin the ideally compensated product crystallized from a melt in which theratio R* applies nevertheless results in a substantial imrovement overthe use of a single solute alone. For the common two-solute systems ofthis invention, reasonable operating ranges of ratio R are considered tobe 0.8R* to 1.2R*. Although this is a preferred operating range, it isseen from the discussion that deviations from this range within thelimits set forth above nevertheless result in an improvement in theuniformity of conductivity characteristics of a crystallizing materialprepared in accordance with this invention as compared with such amaterial solidifying from a melt containing no compensating solute.

The requisite characteristics of solutes 1 and 2 in accordance with thisinvention may be determined from the aseroos discussion and equations.By way of illustration, several suitable combinations are listed below:

In the discussion of instances 1 and 2 of the above table, it is tacitlyassumed that the compensating solute or solute 2 is that which has thegreatest variation in k with variation in growth conditio It should benoted that unlike the processes of instances 3 and 4 the solutepredominating in the liquid or 1n the crystallizing material may beeither solute l or solute 2 as desired and may in fact vary from one tothe other in the solid under certain conditions. Where both solutes areeither acceptors or donors this is of no consequence since the soluteconcentration of concern in the crystallizing material is the sumconcentration.

The processes have been discussed in terms of simple ternary systemscontaining as solutes either one acceptor and one donor, both having kvalues greater than or less than 1, or two solutes of the sameconductivity imparting type, one having a k value of greater than 1 andone having a k value less than 1. Crystals prepared in accordance withthis invention may contain additional solutes. Such solutes maycontribute to the compensation of this invention as in the instance of asolvent material containing a first significant impurity and twoadditional significant impurities, one of which is of oppositeconductivity type and one of Which is of the same conductivity type assolute 1. Additional ingredients may also be included for any of thereasons known to the art as, for example, for the purpose of controllinglifetimes. These processes are not limited to zone-melting operationsbut are applied advantageously to normal freezing operations such as bycrystal pulling. Where the processes are so used, monitoring the growthrate so as to offset varying concentration in the melt may result in agreater constant conductivity portion than is otherwise attainable.Where the compensating solute is of the same conductivity imparting typeand has the other characteristics set forth above the amounts containedin the melt may be so chosen that the increase of the one olfsets thedecrease of the other in the melt in a constant pull rate crystalpulling process so as to result in a substantial constant conductivityportion.

Although the processes have been discussed in terms of random variationsin growth conditions the compensation technique is usefully appliedunder certain steady state conditions. For example where film thicknessA is not uniform at a freezing interface due, for example, to variationsin stirring velocities from one portion of the interface to the other,use of a compensating solute as described herein eifectively securesuniform resistivity over a cross-section corresponding to suchinterface.

What is claimed is:

l. A process of crystallizing semiconductive material evidencing uniformelectrical conductivity characteristics from a body of liquid comprisingas a major ingredient a. fusible extrinsic semiconductive material, andas minor ingredients, two significant solutes, such that one of thecharacteristics, (a) the conductivity imparting type, and (b) the signof the quantity (lk), is opposite for the two solutes, and the other isthe same for the tWo solutes, in which the ratio of the concentration ofsolute 2 in the liquid to that of solute 1 is from 0.8 to 1.2 times theabsolute value of R* where 11* is the ratio of the growth ratecoefiicient of the distribution coefficient of solute l to that ofsolute 2 and in which it is the eifective distribution coefiicient.

2. The process of claim 1 in which the ratio or" the two solutes in theliquid is substantially equal to the absolute value of R.

3. The process of claim 1 in which the body of liquid is a molten zoneof a zone-leveling process.

4. The process of claim 1 in which the body of liquid is the melt of anormal freezing process.

5. The process of claim 4 in which the normal freezing process is acrystal pulling process.

6. The process of claim 1 in which the fusible extrinsic semiconductivematerial is germanium and solute 2 is antimony.

7. The process of claim 6 in which solute l is gallium.

8. The process of claim 1 in which the fusible extrinsic material issilicon and solute 2 is antimony.

9. The process of claim 8 in which solute 1 is gallium.

10. The process of claim 1 in which the fusible extrinsic semiconductivematerial is silicon and the solutes are boron and phosphorus.

11. The process of claim 1 in which the fusible extrinsic semiconductivematerial is germanium and the solutes are boron and gallium.

12. The process of claim 1 in which the fusible extrinsic semiconductivematerial is indium antimonide and the solutes are zinc and cadmium.

No references cited.

1. A PROCESS OF CRYSTALLIZING SEMICONDUCTIVE MATERIAL EVIDENCING UNIFORMELECTRICAL CONDUCTIVITY CHARACTERISTICS FROM A BODY OF LIQUID COMPRISINGAS A MAJOR INGREDIENT A FUSIBLE EXTRINSIC SEMICONDUCTIVE MATERIAL, ANDAS MINOR INGREDIENTS, TWO SIGNIFICANT SOLUTES, SUCH THAT ONE OF THECHARACTERISTICS, (A) THE CONDUCTIVITY IMPARTING TYPE, AND (B) THE SIGNOF THE QUANTITY (1-K), IS OPPOSITE FOR THE TWO SOLUTES, AND THE OTHER ISTHE SAME FOR THE TWO SOLUTES, IN WHICH THE RATIO OF THE CONCENTRATION OFSOLUTE 2 IN THE LIQUID TO THAT OF SOLUTE 1 IS FROM 0.8 TO 1.2 TIMES THEABSOLUTE VALUE OF R* WHERE R* IS THE RATIO OF THE GROWTH RATECOEFFICIENT OF THE DISTRIBUTION COEFFICIENT OF SOLUTE 1 TO THAT OFSOLUTE 2 AND IN WHICH K IS THE EFFECTIVE DISTRIBUTION COEFFICIENT.